Assume that on average, healthy young adults dream 90 minutes each night, as inferred from a number of measures, including rapid eye movement (REM) sleep. An investigator wishes to determine whether drinking coffee just before going to sleep affects the amount of dream time. After drinking a standard amount of coffee, dream time is monitored for each of 28 healthy young adults in a random sample. Results show a sample mean, X, of 88 minutes and a sample standard deviation, s, of 9 minutes.
(a) Use t to test the null hypothesis at the .05 level of significance.
(b) If appropriate (because the null hypothesis has been rejected), construct a 95 percent confidence interval and interpret this interval.